select the correct answer. a student club has 15 members. how many ways can a committee of 6 members be…

Explanation:

Step1: Identify combination formula

The formula for combinations is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items, and $r$ is the number of items to be chosen. Here $n = 15$ and $r=6$.

Step2: Calculate factorial values

$n!=15! = 15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1$, $r!=6!=6\times5\times4\times3\times2\times1$, and $(n - r)!=(15 - 6)!=9!=9\times8\times7\times6\times5\times4\times3\times2\times1$. Then $C(15,6)=\frac{15!}{6!(15 - 6)!}=\frac{15!}{6!9!}=\frac{15\times14\times13\times12\times11\times10\times9!}{6\times5\times4\times3\times2\times1\times9!}$.

Step3: Simplify the expression

Cancel out the $9!$ terms. We have $\frac{15\times14\times13\times12\times11\times10}{6\times5\times4\times3\times2\times1}=\frac{3603600}{720}=5005$.

Answer:

C. 5,005